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a direct N-S numerical solver for "under-resolved" grids.

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Old   May 4, 2017, 03:01
Default a direct N-S numerical solver for "under-resolved" grids.
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I have a question about turbulence modeling of DNS and LES.

For my understanding, in DNS, the grid size should be small enough to resolve the smallest scale(Kolmogorov scale) in turbulent. And then directly solve the N-S equation would simulate the turbulent flow. That is the reason why DNS is too expansive because the number of grids is too much. On the other hand, in LES, the grid size does not need to resolve the Kolmogorov scale. So we could use "more coarse" grid (coarse in the sense that it could be as large as in inertial subrange), and still directly solve N-S equations. However, we need to model the scale smaller than grid size.

My question is, what would happen if we use a numerical solver to directly solve N-S equations (for a high Re number problem) without any turbulent modeling, but the grid size is "small enough" (to get numerical solutions) but not small enough to match Kolmogorov scale?

Does the simulation is not correct completely even though it could demonstrate some "chaotic" or "turbulent-like" flow structure? Or the simulation is correct only for the scale of grid size. The smaller turbulent behavior is lost for scales smaller than grid size?
Thanks for help me.
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Old   May 4, 2017, 03:25
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The "unresolved" DNS is also denoted no-modelled LES and is largely adopted as a test in the LES community. I personally use that to check the additional effect of the SGS model.
For example, you can see these tests

https://www.researchgate.net/publica...blicationTitle
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Old   May 4, 2017, 03:29
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For my understanding you would then perform a so called no-Model LES simulation. You're probably not as accurate as a DNS but your capturing large Eddies which contain already most of the turbulent energy (Energy cascade).

The thing to debate here is, from which grid size on we can define a simulation a Large Eddy Simulation since a CFD simulation on a very coarse grid without additional turbulence model is still technically a no-Model LES.
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Old   May 4, 2017, 03:35
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Depending on the disispative nature of the local truncation error of the adopted discretization, this technique is what is denoted Implicit LES (ILES). The action of the SGS model is actually taken into account by the action of the local truncation error.
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